Qualitative Security Model

In Social Network Principle it is shown that Bitcoin is a network of human relationships. This can be modeled as a directed graph where each vertex represents a merchant and each edge represents a trade for bitcoin. Edges indicate the direction of movement of coin and are quantified in the number of units traded. All owners are presumed to have been merchants at the time of coin receipt, including as miners (selling confirmations) and as recipients of charity (selling goodwill).

If a person is not personally accepting coin, or does not personally validate coin accepted, the person cannot reject invalid coin. The person is entrusting this task to a central authority. Similarly, when a person delegates coin to another party, the person no longer owns the coin. In both cases the person controls only a promise to trade back the coin and therefore does not contribute to security. All people utilizing the same delegate are reduced to just one vertex that represents the delegate.

The graph represents activity occurring in any window of time. While people could decide to withdraw from delegates at some point in time, and validate their own transactions, they cannot act in defense until after they actually do so. The distinction is analogous to being armed vs. having the ability to become armed. As shown in Cockroach Fallacy, the latter matters not when you are getting robbed.

For any period of time, economic security is a function of the number of people and the similarity of amounts traded. The strongest economy would be all people in the world trading for the same number of units in the period, an ideal which can be called a "distributed" economy. The weakest would be one delegate accepting all units traded in the period, which would be a "centralized" economy.

As show in Balance of Power Fallacy, the systemic mining threat is motivated by censorship, not double-spending. Total hash rate is the defense against such attacks, but pooling of hash rate works against the defense. As mining collects into pools it becomes cheaper to co-opt than to compete against it.

Mining decentralization can be defined similarly to economic decentralization. Again we are referring to a social graph. The ideal scenario is every person in the world mining with equal hash power. It is important to security that there is sufficient total hash power to defend against sustained, coordinated, state-level attacks, however decentralization is not security. For a definition of security see the subsequent post.

Each miner is represented by one vertex on the graph. If a miner delegates decision-making to a pool operator, only the operator is represented. The reasoning is the same as with delegation in economic decentralization. The total hash power directed by a miner is the weight (value) of the vertex. There are no edges.

For any period of time, the decentralization of Bitcoin mining is a function of the number of miners and the distribution of hash power they direct during that period. More specifically, the system is strongest which has the greatest number of vertices with the lowest coefficient of variation in weights, or: